A population numbers 15,000 organisms initially and grows by 13.7% each year. Suppose P represents population, and the number of years of growth. An exponential model for the population can be written in the form P = a - b where P-= Question Help: (] Video 1 (3 Video 2 Post to forum Submit Question The fox population in a certain region has an annual growth rate of 8 percent per year. It is estimated that the population in the year 2000 was 28800. (a) Find a function that models the population years after 2000 ( = 0 for 2000). Your answer is P(t) = (b) Use the function from part (a) to estimate the fox population in the year 2008. Your answer is (the answer should be an integer) Question Help: [] Video [ Post to forum Submit Question A vehicle purchased for $25,000 depreciates at a constant rate of 5%. Determine the approximate value of the vehicle 12 years after purchase. Round to the nearest whole dollar. . Question Help: (&) Video [ Post to forum Submit Question A bank features a savings account that has an annual percentage rate of 7 = 5.6% with interest compounded quarterly. Evelyn deposits $5,500 into the account. kt The account balance can be modeled by the exponential formula A(t) = a(l + %) , where 4 is account value after t years , a is the principal (starting amount), r is the annual percentage rate, k is the number of times each year that the interest is compounded. (A) What values should be used for a, r, and k? a= , = , k= (B) How much money will Evelyn have in the account in 8 years? Answer = Round answer to the nearest penny. (C) What is the annual percentage yield (APY) for the savings account? (The APY is the actual or effective annual percentage rate which includes all compounding in the year). APY = %. Round answer to 3 decimal places. Question Help: (2 Video (O Post to forum Submit Question A population of bacteria is growing according to the equation P(t) = 1900e%7. Estimate when the population will exceed 3101. Give your answer accurate to one decimal place. Question Help: []Video 1 (]Video 2 [ Post to forum Submit Question /) =\\ Match each equation with a graph above y = 2(1.26)" . black (K) y = 3(0.88)" . blue (B) y = 3(0.68)" c. green (G) y= 3(1.26):\" d. red (R) y = 3(1.48) e o o Question Help: (] Video { Post to forum Submit Question If all the graphs above have equations with form y = ab\Diseases tend to spread according to the exponential growth model. In the early days of AIDS, the growth factor (i.e. common ratio; growth multiplier) was around 1.8. In 1983, about 1900 people in the U.S. died of AIDS. If the trend had continued unchecked, how many people would have died from AIDS in 20047 (Note: once diseases become widespread, they start to behave more like logistic growth, but don't worry about that for the purpose of this exercise) Question Help: [ Video O Post to forum Submit Question The doubling period of a bacterial population is 15 minutes. At time = 80 minutes, the bacterial population was 80000. What was the initial population at time = 0? :] Find the size of the bacterial population after 4 hours. [:] Question Help: [ Video 1 [ Video 2 [ Post to forum Submit Question Write the equation in exponential form. Assume that all constants are positive and not equal to 1. log(b) = v Question Help: (] Video [ Post to forum Submit Question Write the equation in logarithmic form. Assume that all constants are positive and not equal to 1. 10 =p T m Question Help: []Video [ Post to forum Submit Question Find the logarithm. om0 ] Question Help: (] Video [ Post to forum Submit Question Evaluate using your calculator, giving at least 3 decimal places: o0 Question Help: [ Video [ Post to forum Submit Question Solve for x: 67 = 41 You may enter the exact value or round to 4 decimal places. I used Desmos: https://www.desmos.com/calculator/bk0e55j2xl[ Question Help: DVideo D Post to forum Submit Question\fK R +B + Q Match each equation with a graph above I graphed all 4 at Desmos: https://www.desmos.com/calculator/6mz4n1uq0s [ -v a. red (R) - vlog(x) b. blue (B) -V 10* c. green (G) In(x) d. black (K) Question Help: Video D Post to forum Submit QuestionFind the domain of y = log(7 + 5z). | used symbolab.com ' and typed in "domain of log(3x - 6)" Question Help: [] Video [ Post to forum Submit Question A bacteria culture starts with 740 bacteria and grows at a rate proportional to its size. After 5 hours there will be 3700 bacteria. (a) Express the population P after hours as a function of . Be sure to keep at least 4 significant figures on the growth rate. P(t)- (b) What will be the population after 9 hours? bacteria (c) How long will it take for the population to reach 29707 Give your answer accurate to at least 2 decimal places. Question Help: (&) Video [ Post to forum Submit